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Richard Stephens

Publications and source records attributed to Richard Stephens.

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Intermolecular and Interfacial Origins of Layering in a Near-Isotropic Organic Glass Former

Physical vapor deposition can produce organic glasses with enhanced stability and pronounced structural anisotropy (layering) even when the constituent molecules are nearly spherical. However, the microscopic origin of the layering in spherical molecular glass formers remains unclear. We investigated vapor-deposited films of 9-(3,5-di(naphthalen-1-yl)phenyl)anthracene (α,α-A) by grazing-incidence wide-angle X-ray scattering, atomistic molecular dynamics, and coarse-grained simulations. Experimentally, the layering signal varies nonmonotonically with deposition temperature and is strongest near 0.8T_g. Simulated scattering calculations reproduce the principal experimental features and show that the layering peak does not originate from shifts in single molecule degrees of freedom. In fact, the simulated deposited and bulk glasses show largely the same single-molecule conformations. Interestingly, a one-site coarse-grained liquid with isotropic interactions develops a comparable interfacial layering signature. These results indicate that layering in α,α-A arises primarily from collective density correlations generated at the free surface during deposition rather than from conformational bias or orientational ordering. The findings connect structural anisotropy in vapor-deposited molecular glasses to the generic interfacial organization of simple liquids.

cond-mat.soft↗

Moments and the Range of the Derivative

In this note we introduce three problems related to the topic of finite Hausdorff moments. Generally speaking, given the first n+1 (n in N or n=0) moments, alpha(0), alpha(1),..., alpha(n), of a real-valued continuously differentiable function f defined on [0,1], what can be said about the size of the image of df/dx? We make the questions more precise and we give answers in the cases of three or fewer moments and in some cases for four moments. In the general situation of n+1 moments, we show that the range of the derivative should contain the convex hull of a set of n numbers calculated in terms of the Bernstein polynomials, x^k(1-x)^{n+1-k}, k=1,2,...,n, which turn out to involve expressions just in terms of the given moments alpha(i), i=0,1,2,...n. In the end we make some conjectures about what may be true in terms of the sharpness of the interval range mentioned before.

math.CA↗